The 28-year-old is set to become a free agent in July after deciding not to extend his contract with Amakhosi.
The Umlazi-born goal-minder has been tipped to join the Buccaneers after City revealed that they could not agree on personal terms with Khuzwayo last January.
Recent reports have indicated that Highlands Park have expressed interest in Khuzwayo, who battled for game time at Chiefs due to Itumeleng Khune’s presence at the club.
“He wants to play more than anything,” a source told The Citizen.
Chiefs captain Khune, who is also South Africa’s No.1, was preferred ahead of Khuzwayo at the Soweto giants.
“He feels he has been robbed of a chance to prove his worth as a keeper as he hardly played at Chiefs,” he explained.
It said that Khuzwayo would consider joining Highlands Park if the Tembisa-based club offered him an enticing deal.
“If Highlands can offer him a decent deal, he would consider their offer,” the source concluded.
The Lions of the North secured a promotion back to the PSL after winning the 2017/18 National First Division (NFD) title.
The club has also been linked with experienced keeper Wayne Sandilands, who has fallen out of favour at Pirates.
The 34-year-old began the recent campaign as Pirates' first choice keeper after joining the Soweto giants from Mamelodi Sundowns last July.
However, Sandilands was dropped by Bucs head coach Milutin ‘Micho’ Sredojevic after making a few goalkeeping errors during the 2017/18 season.
Bucs will reportedly offload the former Platinum Stars short-stopper during the upcoming transfer window and sign a young and quality keeper.